An alternating current (AC) electrical grid generally comprises of a network of synchronous machines coupled through a network of transmission lines which deliver the power generated by the synchronous machines to a plurality of customers. A synchronous machine of the type typically used to generate electrical power in an electrical grid includes a movable magnetic element, or rotor, and a number of stationary conductive coils comprising a stator. To generate electrical power, the rotor is coupled to a source of rotational power known as a prime mover and the stator is coupled to a load. Electrical power is provided to the load when the prime mover applies torque to the rotor, which causes the rotor to rotate relative to the stator. The motion of the rotor relative to the stator exposes the stator to a changing magnetic flux, which induces alternating currents in the stator and thereby provides electrical power to the load. The rotational power provided by the prime mover is thereby converted into electrical power at the output terminals of the synchronous machine, with the phase and frequency of the alternating current at the output terminals related to the angular velocity and position of the rotor.
The power exchange between the rotor and the stator of a synchronous machine also operates in reverse. If currents having a leading phase relationship with the rotor are produced in the stator by an external power source, such as by another synchronous machine operating as a generator, the changing magnetic flux produced by the stator may produce a torque moment in the rotor. The synchronous machine may thereby operate as either a generator converting rotational energy into electrical energy (generating mode), or as a motor converting electrical energy into rotational energy (motoring mode) depending on the relationship between the phase of the terminal voltage and the angular position of the rotor. Because of this relationship between rotor position and terminal voltage, when two synchronous machines are connected in parallel and operated as generators to power a common load, the frequency of the rotors will normally become synchronized by electrical interactions between the synchronous machines.
Electrical power generation in present day electrical grids is provided primarily by coupling multiple synchronous machine/prime mover combinations—or synchronous generators—to the grid in parallel. In a typical electrical grid, numerous synchronous generators are located at multiple power plants that utilize various sources of energy to power the prime movers. Examples of commonly employed prime movers include turbines motivated with steam produced by combustion of fossil fuels or heat from nuclear reactions, hydroelectric turbines, and gas fired turbines. The synchronous generators are operated at different geographic locations to provide power to the grid at multiple grid connection points. The collective load presented by the grid is thus much greater than the rated output of any individual synchronous generator. Because of this disparity in the capacity of a single synchronous generator and the capacity of the grid, a single synchronous generator will typically not have an appreciable effect on the grid frequency. The existing grid frequency will thus largely determine the angular velocity of the rotor of a synchronous generator connected to the grid.
When it is desired that the synchronous generator provide more power to the grid, the output of the prime mover is increased, which causes additional torque to be applied to the rotor of the synchronous machine. The increased torque urges the angular position of the rotor forward with respect to the phase of the terminal voltage stator field. The resulting increase in the load angle, also known as the displacement angle, between the internal voltage produced by the field current acting alone and the terminal voltage of the synchronous generator results in an increase in the power provided to the grid. The interrelationship between load angle and power output acts in combination with the kinetic energy stored in the rotating masses of the synchronous generators to impart an inherent flywheel effect to the grid.
The flywheel effect acts as a stability mechanism that contributes to safe and reliable operation of the grid by providing what is known as an inertial response to grid voltage transients. This inertial response is an inherent active power output response by the synchronous generators to grid transient conditions which helps maintain the power balance between the total grid consumption and the total power supplied to the grid. For example, a sudden increase in the load on the grid will typically result in a drop in the frequency of the voltage at the terminals of the synchronous generator, which will initially cause an increase in the load angle. The immediate results of the increase in the load angle include: (1) an increase in the restraining torque provided by the rotor; and (2) an increase in the instantaneous power output of the synchronous generator. The increased restraining torque will oppose the torque supplied by the prime mover and cause the rotor to decelerate so that the load angle begins decreasing back toward its pre-event value. However, the rotational inertia of the synchronous generator will limit the angular acceleration of the rotor, which limits the rate at which the load angle changes as the kinetic energy stored in the synchronous generator is transferred to the grid. Likewise, sudden decreases in grid load may result in a decreased load angle, dropping the instantaneous synchronous generator output and resulting in excess power production being absorbed by an increase in the kinetic energy stored in the rotating masses of the synchronous generator.
The rotating mass of the synchronous generator thus provides an inertial response that slows the rate of change in the grid frequency in response to sudden imbalances between load and production power. By releasing and storing kinetic energy from the rotating masses of the generator, synchronous generators increase grid stability and allow the prime movers time to respond to power imbalances. The larger the total rotating mass in the grid is relative to the change in power demand, the slower the grid frequency will change in response to the power imbalance. Therefore, grids linked with larger numbers of synchronous generators typically provide more stable frequency control by allowing prime mover governors and primary frequency controls more time to respond to changes in power demand.
Wind power generation is an alternative energy source for providing electrical power to the electrical grid. A wind power system may include one or more wind turbines, with a typical wind power system comprising a wind farm having multiple wind turbines ganged together to provide power to the grid at a common location. Wind turbines are typically operated to produce the maximum amount of electrical power possible under the existing wind conditions, which may allow other prime movers connected to the grid to be throttled back to conserve energy. To maximize the aerodynamic efficiency of the wind turbine, the wind turbines is typically operated at an optimal tip speed to wind speed ratio. Because wind speed typically varies considerably over the operating range of the wind turbine, maximizing the aerodynamic efficiency of the wind turbine will cause the rotor speed to vary with wind speed.
To compensate for rotor speed variations, wind turbines are typically coupled to the grid through electronic power converters so that the wind turbine generator may rotate with an angular speed independent of the grid frequency. Electronic power converters convert the variable frequency power produced by the wind turbine into power that is synchronized with the grid voltage. Conventional controllers for electronic power converters are typically designed to cause the converter to transfer power to the electrical grid at a rate that maximizes the instantaneous power output of the wind turbines connected to the converter. Because conventional power electronic converters do not provide an inherent active power response like a synchronous machine, wind turbine power generation systems utilizing conventional power converter controllers do not contribute to the stability of the grid. Thus, transient power imbalances in the grid must be compensated for by the remaining synchronous generators in the power system.
As the demand for wind power increases, the inertial response provided by synchronous generators unrelated to wind turbines will diminish as the total amount of kinetic energy stored in the grid will be less relative to the total capacity of the grid. As a consequence, grid frequency stability may be degraded with increasing wind power penetration into the electrical grid. Faster and larger grid frequency variations can thus be expected as wind power becomes more prevalent, resulting in associated reductions in the stability and reliability of the entire power system.
Thus, there is a need for improved systems, methods, and computer program products for controlling how wind power systems provide power to the grid that maintain the reliability and stability of the electrical grid and allow increased wind power system penetration.